이에 필사적으로 머리를 굴리던 아로니아 영애는 흠흠, 하고 헛기침을 했다. here omg ignore my first reply, that was the wrong one 나는 계속하여 아로니아 영애를 향해 첨예한 눈 도끼를 날렸다. here u go
It's a play on 도끼눈 (as in, sharply shaped eyes). Basically, the speaker was glaring/glowering sharply at Alonia (or however you translated her name). "Glaring daggers" would be a close idiom equivalent.